A formula that can be used to find the coefficient of any term in the expansion of the
nth power of a
binomial of the form (
a +
b).
The coefficients of the expansion of (
a +
b)[latex]^{n}[/latex] can be obtained using the numbers from
Pascal's triangle.
Examples
(a + b)[latex]^{1}[/latex] = (a + b)
(a + b)[latex]^{2}[/latex] = a[latex]^{2}[/latex] + 2ab + b[latex]^{2}[/latex]
(a + b)[latex]^{3}[/latex] = a[latex]^{3}[/latex] + 3a[latex]^{2}[/latex]b + 3ab[latex]^{2}[/latex] + b[latex]^{3}[/latex]
(a + b)[latex]^{4}[/latex] = a[latex]^{4}[/latex] + 4a[latex]^{3}[/latex]b + 6a[latex]^{2}[/latex]b[latex]^{2}[/latex] + 4ab[latex]^{3}[/latex] + b[latex]^{4}[/latex]
